The present invention relates to a method and apparatus for teaching the playing of unfretted stringed instruments in the violin family such as the violin, viola, cello and bass. More specifically, the present invention provides a method for teaching the design, organization, structure and use of the fingerboard of such instruments and a chart that is useful in conjunction with that method to illustrate the location of pitches and corresponding fingering on the fingerboard while playing such an instrument.
Instrument Construction
Stringed instruments in the violin family generally consist of a neck and a hollow, resonating body attached to one end of the neck. Four strings extend from the opposite end of the neck (the xe2x80x9cpeg boxxe2x80x9d) over what is referred to as a nut to a bridge positioned on the mid portion of the body to a tailpiece positioned on the far end of the body. The strings extend over a fingerboard which extends along the front of the neck and the top portion of the body. A bow is used to vibrate the strings over the body, wherein the sound resonates. Specific pitches are produced on each string by drawing the bow over the strings and xe2x80x9cstoppingxe2x80x9d the string by the player placing a finger at specific locations on the string along the fingerboard. By stopping a string at any point, the length of the vibrating portion of the string changes, resulting in a higher (shorter vibrating string portion) or a lower (longer vibrating string portion) pitch. In order to produce the desired notes, the player must be able to place his/her fingers on the strings at the appropriate locations on the fingerboard.
Acoustical Characteristics, Resonance Pattern
The vibrating string of an unfretted, bowed stringed instrument produces a complex musical tone that is composed of the basic frequency of the vibrating string and a series of higher frequencies. The basic frequency of the vibrating string is called the xe2x80x9cfundamental.xe2x80x9d The frequencies that are produced simultaneously with the fundamental are called the xe2x80x9covertone seriesxe2x80x9d or xe2x80x9charmonic series.xe2x80x9d An individual note in an overtone series or a harmonic series is referred to as an xe2x80x9covertonexe2x80x9d or a xe2x80x9charmonic,xe2x80x9d respectively. The fundamental plus the overtone series comprise a complex musical tone.
The overtones produced in a given complex tone vibrate at frequencies that are whole number multiples of the frequency of the fundamental. For instance, in the case of the open A string of a cello, the fundamental frequency is 220 cycles per second, the xc2xd string harmonic is 440 cycles per second (2xc3x97220), the ⅓ string harmonic is 660 cycles per second (3xc3x97220), the xc2xc string harmonic is 880 cycles per second (4xc3x97220), and the ⅙ string harmonic is 1320 cycles per second (6xc3x97220).
Each pitch played on the instrument is a complex tone that is comprised of the fundamental frequency and a complete overtone series. Harmonics can be played on any string by touching the string lightly with one finger at specific points that correspond to the overtones in the series. The location of each harmonic point (xe2x80x9cnodexe2x80x9d) divides the vibrating string into precise fractional segments that correspond with the ratio between the fundamental frequency and one of the corresponding overtone frequencies. For instance, the xc2xd string harmonic divides the string into two equal vibrating parts and produces a frequency equal to two times the fundamental frequency. Similarly, the ⅓ string harmonic divides the string into three equal parts and produces a frequency equal to three times the fundamental frequency; the xc2xc string harmonic divides the string into four equal parts and produces a frequency equal to four times the fundamental frequency; and the ⅙ string harmonic divides the string into six equal parts and produces a frequency equal to six times the fundamental frequency. The harmonics divide each string into six harmonic regions: the first is located from the first or upper xc2xc string harmonic and above, the second between the upper ⅓ and xc2xd string harmonics, the third between the xc2xd and lower ⅓ string harmonics, the fourth between the lower ⅓ and lower xc2xc string harmonics, the fifth between the lower xc2xc and lower ⅙ string harmonics, and the sixth below the lower ⅙ string harmonic. The complete sequence of natural tones is contained within each harmonic region.
Harmonics are located at the same points on each string. The same frequency ratio with the fundamental frequency is consistent on all strings. Each harmonic can be played individually.
A harmonic pitch is fixed according to the frequency ratio of the overtone series. Therefore, harmonics can be used as reliable reference points, or landmarks, for accurate pitch and the location of other pitches along a string.
The characteristic sound of a complex tone is a blend of the fundamental and the overtones in the series. The strongest and most easily heard overtones are produced at the xc2xd string harmonic, ⅓ string harmonic and xc2xc string harmonic locations. Other overtones exist but are difficult to hear individually or are beyond the range of the ear.
An xe2x80x9cintervalxe2x80x9d is the distance between two notes that are played simultaneously or separately. Each note in an interval is a complex tone with a distinct overtone series. The intervals that are most strongly related to the overtone series are the unison and the octave. A unison is comprised of two pitches with the same frequency. An octave is comprised of two pitches in which the upper note has a frequency twice that of the lower pitch.
When a string is vibrated at a frequency that is the same as, or is a whole number multiple of, another open (i.e., unstopped) string on the instrument, a xe2x80x9csympathetic vibrationxe2x80x9d will be imparted to the other strings. The note or tone produced by the other strings will reinforce or enrich the note or tone produced by the first string to produce a condition called xe2x80x9cresonance.xe2x80x9d Resonance creates a particularly appealing sound, and verifies accurate pitch (xe2x80x9cplaying in tunexe2x80x9d) for the player. If the frequencies of the two interval notes do not match (i.e., are not a precise whole number multiple ratio), sympathetic resonance of the sound is reduced. The pitch is referred to as xe2x80x9cout of tune.xe2x80x9d The degree to which pitches are adjusted to produce maximum resonance is referred to as xe2x80x9cintonation.xe2x80x9d
Fingerboard Geography and Finger Logic
The location of pitches along a string (xe2x80x9cfingerboard geographyxe2x80x9d) and the corresponding placement of the player""s fingers on the strings along the fingerboard must be learned by the player more or less intuitively since there are no visual reference points along the fingerboard (such as frets in the case of a guitar) to signal the player as to the appropriate location of the various pitches along the fingerboard.
In addition, learning the correct location and name of each pitch, and understanding the arrangement of notes on the fingerboard, is learned through the ear, hand/touch and visual memory. Individual pitches (notes with the same frequency) can be played at various locations on the fingerboard, on different strings (xe2x80x9calternate fingeringsxe2x80x9d). Knowing the arrangement of the possible notes on the entire fingerboard (xe2x80x9cfingerboard geographyxe2x80x9d) and the corresponding fingering while playing notes on one string and across strings (xe2x80x9cfinger logicxe2x80x9d) is an important factor in learning to play such an instrument.
The prior art methods of teaching the playing of a bowed, unfretted stringed instrument generally teach the location of pitches and the corresponding finger locations with reference to the location of the player""s left hand along the fingerboard. The possible hand positions are referenced as xe2x80x9cxc2xdxe2x80x9d, xe2x80x9c1stxe2x80x9d, xe2x80x9c2ndxe2x80x9d, xe2x80x9c3rdxe2x80x9d, xe2x80x9c4thxe2x80x9d, xe2x80x9c5thxe2x80x9d, xe2x80x9c6thxe2x80x9d, xe2x80x9c7thxe2x80x9d and xe2x80x9cthumbxe2x80x9d (in the case of cello and bass only) positions. Within each position, the fingers can play a range of notes on one string and by moving across the strings. Knowing the names, location and interval sizes (i.e., unison, octave, etc.) of each note within a designated range is referred to as xe2x80x9cfinger logic.xe2x80x9d The distance that the fingers can reach on one string without moving to a new position is called xe2x80x9chand span.xe2x80x9d This distance is measured in terms of half steps which correspond with the distance from one key to an adjacent key on a piano keyboard. With reference to the cello, each finger covers the distance of a half step. The distance from the index (first) finger to the little (fourth) finger is three half steps. The 1st position on the cello, for instance, is the hand position along the fingerboard where the index finger stops a string to play a pitch one whole step (two half steps) above the pitch produced on that string when it is unstopped or open. The little finger stops the string three half steps above the index finger. Similarly, the 4th position is the hand position where the index finger stops a string to play a pitch that is five tones (seven half steps) above the pitch produced by that open string. The little finger stops the string three half steps above the index finger and ten half steps above the open string.
These methods typically employ xe2x80x9cfingerboard mapsxe2x80x9d intended to show the player the appropriate location of any given note and the corresponding fingering with respect to each hand position and a visual representation of the pitch/note using standard musical notation. Such fingerboard maps typically consist of a graphic depiction of the finger placement of each note for each hand position. These fingerboard maps are generally meant to be placed in front of the student while the instrument is played to be used as a reference rather than as read as music.
The fingerboard maps of the prior art either show the finger position of the various notes possible for each hand position on each fingerboard map, in which case a large number of fingerboard maps must be presented to the student to show the number of notes that might be played in that hand position, or a large number of hand positions and the corresponding notes must be shown on the same fingerboard map. In either case, the large amount of information conveyed to the student is difficult to sort out while playing the instrument and, as a result, difficult to learn.
In addition, the visual representation of the pitches/notes on such fingerboard maps is often difficult to translate into actual finger placement on the fingerboard while playing the instrument because of the different orientation of the fingerboard map and the fingerboard from the student""s perspective. For instance, a fingerboard map may be placed on a vertical surface in front of the student (such as a wall) with the depiction of the fingerboard extending from left to right or from top to bottom. The player, however, will have a different orientation of the fingerboard when the instrument is held for playing. It is often difficult for the student to translate the finger position from that shown on the fingerboard map to the actual fingerboard because of that different orientation.
The present invention is designed to present information to the student relating to the proper location of pitches and placement of fingers on the strings of an unfretted, bowed stringed instrument in a manner that is easily and quickly understood by the student.
It is one object of the present invention to provide a method of and apparatus for teaching the use or playing of an unfretted, bowed stringed instrument by reference to the location of the harmonics and resonant tones of the instrument as opposed to the location of the notes that can be played from any particular hand position.
It is another object of the present invention to provide a method of and apparatus for teaching the use or playing of an unfretted, bowed stringed instrument wherein the location of the resonant tones, harmonics and corresponding finger locations are easily and readily identified as reference points for accurate pitch.
It is another object of the present invention to provide a xe2x80x9csound mapxe2x80x9d depicting the finger locations of resonant tones and harmonics with respect to the fingerboard of an unfretted, bowed stringed instrument.
It is another object of the present invention to provide a xe2x80x9csound mapxe2x80x9d depicting the finger locations of natural and sharp/flat notes with respect to the fingerboard of an unfretted, bowed stringed instrument, wherein the natural notes and the sharp or flat notes (chromatic) are readily and easily distinguishable from one another.
It is another object of the present invention to provide a method of and apparatus for teaching the use or playing of an unfretted, bowed stringed instrument wherein identical notes playable at different locations along the fingerboard are similarly displayed to the player for easy and ready identification as alternative finger locations for such notes.
It is yet another object of the present invention to provide for alternative perspectives of a xe2x80x9csound mapxe2x80x9d according to the present invention to accommodate varying perspectives of different players.
To those ends, a chromatic fingerboard map is provided which illustrates the relative location of the various notes within the playing range of an unfretted, bowed stringed instrument. The fingerboard map illustrates the entire fingerboard of the instrument extending from the top (corresponding to the top of the fingerboard along the neck of the instrument) to the bottom (corresponding to the bottom of the fingerboard near the bridge). The map designates each of the four strings of the instrument and the name of each open string, labeled from low to highxe2x80x94C, G, D and A. The approximate location of the shoulder of the body of the instrument is shown for reference by the player. Along each string, the relative location for each pitch is shown. The locations of the natural notes (corresponding with the white keys on a piano) are shown by one type of symbol or indicia (i.e., a square) while the locations of the sharp/flat notes (corresponding to the black keys on a piano) are shown by another type of symbol or indicia (i.e., a circle). The fingerboard map is divided into four regions each defined by the location of the xc2xd, ⅓ and xc2xc string harmonics located along the fingerboard. The location of the resonant tones within each region are color coded (i.e., green, pink, blue and yellow) in such a manner that the corresponding resonant tones in each region are shown in the same color. In addition, the harmonics are designated by a third symbol or indicia (i.e., a star) for easy identification.
The present invention solves the problem of the fingerboard maps of the prior art in that, while it contains a complete set of information as to the location of all notes within the playing range of the instrument, such information is readily discernable with respect to any individual note because of the manner in which the information is visually presented.